TSTP Solution File: ANA034-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA034-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:46:46 EDT 2022
% Result : Unsatisfiable 1.73s 1.95s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 29 ( 20 unt; 0 nHn; 24 RR)
% Number of literals : 45 ( 4 equ; 20 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 24 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(A)
| ~ c_lesse_quals(B,C,A)
| ~ c_lesse_quals(D,E,A)
| ~ c_lesse_quals(c_0,B,A)
| ~ c_lesse_quals(c_0,E,A)
| c_lesse_quals(c_times(D,B,A),c_times(E,C,A),A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(A)
| ~ c_lesse_quals(c_0,B,A)
| ~ c_lesse_quals(c_0,C,A)
| c_lesse_quals(c_0,c_times(C,B,A),A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_less(B,C,A)
| c_lesse_quals(B,C,A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_lesse_quals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| class_Orderings_Oorder(A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__cancel__semiring(A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA034-2.p',unknown),
[] ).
cnf(12,axiom,
c_less(c_0,v_c,t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(13,axiom,
c_lesse_quals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(14,axiom,
c_lesse_quals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(16,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(17,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(18,plain,
~ c_lesse_quals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),16]),
[iquote('back_demod,6,demod,16')] ).
cnf(19,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[17,10]),
[iquote('hyper,17,10')] ).
cnf(20,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(hyper,[status(thm)],[17,9]),
[iquote('hyper,17,9')] ).
cnf(21,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(hyper,[status(thm)],[17,8]),
[iquote('hyper,17,8')] ).
cnf(23,plain,
c_HOL_Oabs(c_times(A,B,t_b),t_b) = c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b),
inference(hyper,[status(thm)],[17,1]),
[iquote('hyper,17,1')] ).
cnf(24,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),23]),
[iquote('back_demod,18,demod,23')] ).
cnf(26,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),23])]),
[iquote('back_demod,15,demod,23,flip.1')] ).
cnf(27,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),26]),
[iquote('back_demod,24,demod,26')] ).
cnf(28,plain,
class_Orderings_Oorder(t_b),
inference(hyper,[status(thm)],[19,7]),
[iquote('hyper,19,7')] ).
cnf(29,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(hyper,[status(thm)],[19,5]),
[iquote('hyper,19,5')] ).
cnf(30,plain,
c_lesse_quals(c_0,v_c,t_b),
inference(hyper,[status(thm)],[28,4,12]),
[iquote('hyper,28,4,12')] ).
cnf(34,plain,
c_lesse_quals(c_0,c_times(v_c,c_HOL_Oabs(A,t_b),t_b),t_b),
inference(hyper,[status(thm)],[29,3,21,30]),
[iquote('hyper,29,3,21,30')] ).
cnf(97,plain,
c_lesse_quals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[14,2,20,13,29,34]),26]),
[iquote('hyper,14,2,20,13,29,34,demod,26')] ).
cnf(98,plain,
$false,
inference(binary,[status(thm)],[97,27]),
[iquote('binary,97.1,27.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ANA034-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 10:17:21 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.73/1.95 ----- Otter 3.3f, August 2004 -----
% 1.73/1.95 The process was started by sandbox2 on n027.cluster.edu,
% 1.73/1.95 Wed Jul 27 10:17:22 2022
% 1.73/1.95 The command was "./otter". The process ID is 28074.
% 1.73/1.95
% 1.73/1.95 set(prolog_style_variables).
% 1.73/1.95 set(auto).
% 1.73/1.95 dependent: set(auto1).
% 1.73/1.95 dependent: set(process_input).
% 1.73/1.95 dependent: clear(print_kept).
% 1.73/1.95 dependent: clear(print_new_demod).
% 1.73/1.95 dependent: clear(print_back_demod).
% 1.73/1.95 dependent: clear(print_back_sub).
% 1.73/1.95 dependent: set(control_memory).
% 1.73/1.95 dependent: assign(max_mem, 12000).
% 1.73/1.95 dependent: assign(pick_given_ratio, 4).
% 1.73/1.95 dependent: assign(stats_level, 1).
% 1.73/1.95 dependent: assign(max_seconds, 10800).
% 1.73/1.95 clear(print_given).
% 1.73/1.95
% 1.73/1.95 list(usable).
% 1.73/1.95 0 [] A=A.
% 1.73/1.95 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)=c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a).
% 1.73/1.95 0 [] -class_Ring__and__Field_Opordered__semiring(T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_0,V_c,T_a)| -c_lesse_quals(c_0,V_b,T_a)|c_lesse_quals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a).
% 1.73/1.95 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)| -c_lesse_quals(c_0,V_b,T_a)| -c_lesse_quals(c_0,V_a,T_a)|c_lesse_quals(c_0,c_times(V_a,V_b,T_a),T_a).
% 1.73/1.95 0 [] -class_Orderings_Oorder(T_a)| -c_less(V_x,V_y,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 1.73/1.95 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.73/1.95 0 [] c_less(c_0,v_c,t_b).
% 1.73/1.95 0 [] c_lesse_quals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b).
% 1.73/1.95 0 [] c_lesse_quals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.73/1.95 0 [] c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)=c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.73/1.95 0 [] -c_lesse_quals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b).
% 1.73/1.95 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.73/1.95 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T)|class_Orderings_Oorder(T).
% 1.73/1.95 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__cancel__semiring(T).
% 1.73/1.95 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.73/1.95 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.73/1.95 end_of_list.
% 1.73/1.95
% 1.73/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.73/1.95
% 1.73/1.95 This is a Horn set with equality. The strategy will be
% 1.73/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.95 sos and nonpositive clauses in usable.
% 1.73/1.95
% 1.73/1.95 dependent: set(knuth_bendix).
% 1.73/1.95 dependent: set(anl_eq).
% 1.73/1.95 dependent: set(para_from).
% 1.73/1.95 dependent: set(para_into).
% 1.73/1.95 dependent: clear(para_from_right).
% 1.73/1.95 dependent: clear(para_into_right).
% 1.73/1.95 dependent: set(para_from_vars).
% 1.73/1.95 dependent: set(eq_units_both_ways).
% 1.73/1.95 dependent: set(dynamic_demod_all).
% 1.73/1.95 dependent: set(dynamic_demod).
% 1.73/1.95 dependent: set(order_eq).
% 1.73/1.95 dependent: set(back_demod).
% 1.73/1.95 dependent: set(lrpo).
% 1.73/1.95 dependent: set(hyper_res).
% 1.73/1.95 dependent: clear(order_hyper).
% 1.73/1.95
% 1.73/1.95 ------------> process usable:
% 1.73/1.95 ** KEPT (pick-wt=17): 1 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs(c_times(B,C,A),A)=c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).
% 1.73/1.95 ** KEPT (pick-wt=28): 2 [] -class_Ring__and__Field_Opordered__semiring(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(D,E,A)| -c_lesse_quals(c_0,B,A)| -c_lesse_quals(c_0,E,A)|c_lesse_quals(c_times(D,B,A),c_times(E,C,A),A).
% 1.73/1.95 ** KEPT (pick-wt=17): 3 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)| -c_lesse_quals(c_0,B,A)| -c_lesse_quals(c_0,C,A)|c_lesse_quals(c_0,c_times(C,B,A),A).
% 1.73/1.95 ** KEPT (pick-wt=10): 4 [] -class_Orderings_Oorder(A)| -c_less(B,C,A)|c_lesse_quals(B,C,A).
% 1.73/1.95 ** KEPT (pick-wt=8): 5 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.73/1.95 ** KEPT (pick-wt=24): 6 [] -c_lesse_quals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b).
% 1.73/1.95 ** KEPT (pick-wt=4): 7 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|class_Orderings_Oorder(A).
% 1.73/1.95 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__cancel__semiring(A).
% 1.73/1.95 ** KEPT (pick-wt=4): 9 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.73/1.95 ** KEPT (pick-wt=4): 10 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.73/1.95
% 1.73/1.95 ------------> process sos:
% 1.73/1.95 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.73/1.95 ** KEPT (pick-wt=4): 12 [] c_less(c_0,v_c,t_b).
% 1.73/1.95 ** KEPT (pick-wt=13): 13 [] c_lesse_quals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b).
% 1.73/1.95 ** KEPT (pick-wt=13): 14 [] c_lesse_quals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.73/1.95 ** KEPT (pick-wt=31): 15 [] c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)=c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.73/1.95 ---> New Demodulator: 16 [new_demod,15] c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)=c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b).
% 1.73/1.95 ** KEPT (pick-wt=2): 17 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.73/1.95 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.73/1.95 >>>> Starting back demodulation with 16.
% 1.73/1.95 >> back demodulating 6 with 16.
% 1.73/1.95
% 1.73/1.95 ======= end of input processing =======
% 1.73/1.95
% 1.73/1.95 =========== start of search ===========
% 1.73/1.95
% 1.73/1.95 -------- PROOF --------
% 1.73/1.95
% 1.73/1.95 ----> UNIT CONFLICT at 0.00 sec ----> 98 [binary,97.1,27.1] $F.
% 1.73/1.95
% 1.73/1.95 Length of proof is 13. Level of proof is 5.
% 1.73/1.95
% 1.73/1.95 ---------------- PROOF ----------------
% 1.73/1.95 % SZS status Unsatisfiable
% 1.73/1.95 % SZS output start Refutation
% See solution above
% 1.73/1.95 ------------ end of proof -------------
% 1.73/1.95
% 1.73/1.95
% 1.73/1.95 Search stopped by max_proofs option.
% 1.73/1.95
% 1.73/1.95
% 1.73/1.95 Search stopped by max_proofs option.
% 1.73/1.95
% 1.73/1.95 ============ end of search ============
% 1.73/1.95
% 1.73/1.95 -------------- statistics -------------
% 1.73/1.95 clauses given 16
% 1.73/1.95 clauses generated 86
% 1.73/1.95 clauses kept 94
% 1.73/1.95 clauses forward subsumed 13
% 1.73/1.95 clauses back subsumed 0
% 1.73/1.95 Kbytes malloced 1953
% 1.73/1.95
% 1.73/1.95 ----------- times (seconds) -----------
% 1.73/1.95 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.73/1.95
% 1.73/1.95 That finishes the proof of the theorem.
% 1.73/1.95
% 1.73/1.95 Process 28074 finished Wed Jul 27 10:17:23 2022
% 1.73/1.95 Otter interrupted
% 1.73/1.95 PROOF FOUND
%------------------------------------------------------------------------------